"Economics is the field that has used game theory the most broadly to
understand bargaining, pricing, firm competition, incentive contracts, and
more," explains [Colin] Camerer,... Professor of Behavioral Economics in
Caltech's Division of Humanities and Social Sciences. "Almost all the analysis,
however, assumes people plan ahead and carefully figure out what others will do,
which often results in mathematical claims that are highly unrealistic
cognitively."

In reality, Camerer says, a key part of strategizing about what other
people--or corporations, or countries--will do involves thinking about what they
think you will do. "You can also think about what others think you think. . . .
It can go on and on."

Research by Camerer and others--including Teck Ho at the University of
California, Berkeley, and Kuan Chong from the National University of
Singapore--into this form of strategizing has led to what Camerer calls the
"cognitive hierarchy theory."

"The cognitive hierarchy theory finds that people only do a few steps of this
kind of iterated thinking," he explains. "Usually, it's just one step: I act as
if others are unpredictable. But sometimes it's two steps: I act as if others
think *I* am unpredictable. You can think of the number of steps a person takes
as their strategic IQ. A higher strategic IQ means you are outthinking a lot of
other people."

Most of us have a pretty low strategic IQ, but that's to be expected, Camerer
notes. To reach a truly high strategic IQ requires either special experience
with a particular type of game (such as poker), training, or, in rare cases,
special gifts.

The cognitive hierarchy theory has been tested using many different
game-theory experiments, as well as field-data sets. One such data set, Camerer
says, is the Swedish LUPI lottery in which everyone picks a number from one to
99,999, and the lowest unique positive integer wins. "In this game you want to
pick a low number, but one that is also a number nobody else will think of," he
notes.

With more than 2.5 million observations to analyze--as well as a laboratory
recreation of the lottery using numbers 1 to 99--Camerer and his colleagues from
Caltech, the Stockholm School of Economics, and the National Taiwan University
say the results fit extremely well with the original theory. If people were
accurately guessing what everyone else would do, they would pick numbers from 1
to 5000 with equal frequency, and rarely pick any higher numbers. The Swedish
players, however, chose lower numbers--numbers below 1000--much too often, from
a strategic point of view. "This pattern is consistent with people doing two to
three steps of thinking," Camerer says.

Camerer and colleagues have also been looking at how people make economic
decisions when they are not given sufficient information to make an informed
choice. "What should you infer about a restaurant with an online menu that
doesn't have prices?" he asks. If you guessed that their prices are high, you'd
probably be right. "And yet," says Camerer, "there are a number of people who
could conclude that leaving prices off doesn't mean anything."

Or take the example Camerer studies, along with Caltech PhD alumnus Alex
Brown (now at Texas A&M University) and Dan Lovallo, from the University of
Western Australia--that of movies released without first being shown to critics,
a process known as a "cold opening." To test their theory Camerer and colleagues
looked at all 850 widely-released movies in the U.S. from 2000 through 2006.

"Usually, the movies that are not shown in advance are below-average movies
as ultimately rated by both critics and moviegoers," says Camerer. "But there is
a 15 percent increase in box office revenue from not first showing the movie."

The reason for this boost in ticket sales? Camerer thinks it has to do with
people who don't think strategically--who don't have high strategic IQs. "We
think it means you can fool some of the people some of the time," he says.
"Specifically, you can fool the people who don't pay attention to reviews and
who also don't realize that not wanting to show a movie to critics is a bad
sign."

Camerer notes that cognitive hierarchy theory can be used by people and
businesses to forecast more accurately what other people are likely to do in
various situations; they can then use those forecasts to make better choices.
"For instance," he says, "the data about cold openings could be used by the
movie industry to retrospectively forecast whether they should have held a movie
back from the critics." It could also help them to decide what to do in future
cases to maximize their profits.

"Economics is the field that has used game theory the most broadly to
understand bargaining, pricing, firm competition, incentive contracts, and
more," explains [Colin] Camerer,... Professor of Behavioral Economics in
Caltech's Division of Humanities and Social Sciences. "Almost all the analysis,
however, assumes people plan ahead and carefully figure out what others will do,
which often results in mathematical claims that are highly unrealistic
cognitively."